I have many sets of English (inch) sized drill bits as well as a couple of metric sets.
On the English (inch) sets the sequences vary. Fractional bits come in 1/64" steps or 0.0156". That is probably the best choice of all the sets. Number and letter sized bits seem to have NO real sequence. Some adjacent sizes in the number sizes are only 0.0002" (no error) apart while other, number sizes are as much as 0.0065" apart. And there is absolutely no discernible pattern. I am sure there is a reason for this awful sequence, but it is going to require a long, long explanation if you include all the details.
In the metric bits, one of my sets is in 1 mm steps and the other is in 0.5 mm steps. While this is a lot better than the number and letter sizes, it is by no means ideal. I checked and saw that metric bits are available in 0.1mm steps. That seems to cover the range from 1 or 2mm up to, perhaps 20mm fairly well. But I have not seen any index boxes for such a collection. Contrast this to the 101 bit sets of letter, number, and fraction bits which are fairly common.
There are two main types of sequence that seem to make sense here: arithmetic (constant difference/added amount) and logarithmic (constant factor - multiple). Each of these has it's advantages and drawbacks.
The arithmetic or constant difference sequence may be good at some sizes, but no matter how well you choose the starting point, it will always become difficult to follow at both larger and smaller ones. For instance, the 1/64" sequence of fractional sized bits may be quite good between 3/16" and 1" but comes to an abrupt end at the 1/64" size as it would be followed by 0". And who ever saw, even in catalogs, a 3 1/64" bit? Such a small size increase above 3" is never needed in most shops and almost useless. Many fractional bit sets may start with 1/64" increments at the low end, but switch to 1/32" or even 1/16" around the 1/4" size and end with 7/8" followed by 1" instead of 15/64". That is the nature of arithmetic sequences. When applied to practical matters, they fail at both ends (high and low).
On the other hand, a logarithmic sequence is difficult at almost all values. Consider: for both English and metric sizes a 0.5X or 2X (same thing, just different directions) jump would easily leave too much of a gap. 1/16", 1/8", 1/4", 1/2", 1", etc. or 1mm, 2mm, 4mm, 8mm, 16mm, etc. are both just too widely spaced to be of much use. A smaller multiple would be clearly needed. But WHAT would that be? A factor of 4/3X that starts at a nice, whole number like 1, would result in a sequence that almost never returns to whole numbers. 5/4X also rapidly goes into long decimal places at the low end: 1, 0.8, 0.64, 0.512, 0.4096, 0.32768, etc. 1mm, 0.8mm, may be OK, but 0,512mm or 0.32768mm? This is bad in two ways, horrible decimal values and gaps that are still too large. Who would want that? Clearly a smaller multiplier/divisor would be needed. BUT WHAT.
One place where a logarithmic ratio has been implemented with success is in the electronics field. Things like resistor values follow such a sequence. There are several logarithmic sequences that are used. And they actually have names: E6, E12, E24, E48, E96, etc. They are based on using a common factor (a logarithmic ratio) between sizes. The E12 is, perhaps the most common. Each value is 1.12X the previous one and it's values are 1, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2, and 10. That comprises one decade of values. Other decades are simply multiplies of 10 of those values" 10, 12, 15, etc. and 100, 120, 150, etc. and 0.1, 0.12, 0.15, etc. So the sequence is easily defined by just the numbers for a single decade. The numbers above are not the exact values given by the power equation that actually defines the sequence. They are rounded to the nearest two digits and that makes them a lot more acceptable to the users.
The other E
xx sequences are sub-sets or super-sets of the E12. So the E6 sequence (a sub-set of E12) has every other value of the E12 sequence: 1, 1.5, 2.2, 3.3, 4.7, 6.8, and 10. And the E24 sequence, which is used for 5% resistor values, is: 1, 1.1, 1.2, 1.3 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1, and 10. Again, the values are rounded to two places. In both the E12 and E24 sequences the rounding errors produce differences from the nominal values which are evenly spaced by factors of 1.12115... and 1.10069... respectively.
As a clue to how these numbers work in practice, you may notice that the E12 values are approximately at 12% internals while the E24 values are about 5% apart. Not surprisingly, the E12 values are called the 10% series and the E24 the 5% series. These values, when combined with the 10% or 5% specification, just about overlap. A 5%, E24 resistor that is marked 2.2 Ohms, +/-5% will have a value between 2.1 and 2.3 Ohms. The 2.0 Ohm, 5% ones will be between 1.9 and 2.1 Ohms and the 2.4 Ohm, 5% one between 2.3 and 2.5 Ohms. All of these ranges are about +/-5%. The practical result, at least for a manufacturer of resistors, is that any, EVERY resistor that comes off the manufacturing line can be sorted into one or another of the standard values in that (actually in any) standard sequence. There is zero waste as every item made is within +/-5% of one of the values. Or +/- 10% for the E12 values, etc. No matter how bad their equipment, materials, or methods they CAN NOT make a resistor that can't be accurately marked with one of the values. Smart, right?
But E6 is a very coarse sequence and even E12 would be too coarse for drill bit sizes. We would have to step up to an E24 or E48 to get a reasonable one. The E24 sequence, applied to metric drill bit sizes might be: 1, 1.1, 1.2, 1.3 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1, and 10. Then 11, 12, etc. Probably still a bit too coarse for machinist use. So E48 may be the smallest sequence to consider here and that one is going to have three digit values. And if you look at a table of them, then you will see that those numbers do not have anything nice about them.
Also 10%, 5%, and probably 2% (the E48 sequence is referred to as 2%) values are not going to meet the accuracy needs of machinists. A 5mm bit +/- 0.1mm (+/- 0.002") is worse than even those routinely found at hardware store or home supply places.
I fear that no sequence that is based on any single, simple rule is going to meet our needs. But we can wish.
Standard Resistor Values In 1952, the IEC (International Electrotechnical Commission) decided to define the resistance and tolerance values into a norm, to ease the mass manufacturing of resistors.…
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